Number worksheet — GCSE Higher

1.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

2.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

3.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

4.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

5.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

6.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

7.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

8.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

9.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

10.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

11.Given that 2⁵ = 32, work out 2⁶.

12.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.

13.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

14.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

15.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.